Lecture 12, existence and nonexistence for semilinear elliptic problems

On January 16th, we have discussed various existence and non-exisetnce results for semilinear elliptic equations:

(1) The Pokhozayev identity and nonexistence for solutions of $-\Delta u = |u|^{p-1} u$ for sufficiently large $p$;

(2) The sub- and supersolution method (cf. Evans, Chapter 9.3 and Theorem 1 there);

(3) The solutions of the 4th list of problems, providing in fact the proof of Theorem 3 in Evans, Chapter 8.5.2.